The Borel summable solutions of heat operators on a real analytic manifold

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:410

Article

Lysik, Grzegorz^1,2 

[1] Polish Acad Sci, Inst Math, PL-00956 Warsaw 10, Poland

[2] Jan Kochanowski Univ, Kielce, Poland

关键词: Heat operators;    Commuting vector fields;    Borel summability;    Integral means;    Pizzetti's formulas;   

DOI  :  10.1016/j.jmaa.2013.08.011

来源: Elsevier

【 摘 要 】

We study heat type equations partial derivative(t)u = (Delta) over tildeu, where the operator (Delta) over tilde is given by a sum of squares of commuting, real analytic vector fields acting on a real analytic manifold. We give necessary and sufficient conditions for convergence and Borel summability of formal power series solutions in terms of generalized integral means of the initial data. The results are also valid for affine perturbations of (Delta) over tilde. (C) 2013 Published by Elsevier Inc.

【 授权许可】

Free